Question

Find the value(s) of $k$ so that $PQ$ will be parallel to $RS$. given:
(i) $P(2,4),Q(3,6),R(8,1)\text{and}S(10,k)$

Answer 1

Given,
$P(2,4),Q(3,6),R(8,1)\text{and}S(10,k)$

We know that, slope of line $=\frac{y_2-y_1}{x_2-x_1}$

$\therefore$ Slope of $PQ=\frac{6-4}{3-2}=2$

And, Slope of $RS=\frac{k-1}{10-8}=\frac{k-1}{2}$

As PQ and RS are parallel.

So, slopes are equal to each other.

$\therefore$ Slope of PQ = Slope of RS

$\Rightarrow 2=\frac{k-1}{2}$

$\Rightarrow k-1=4$

$\therefore k=5$

Hence, the value of $k$ is 5.